Long only 1/n portfolio

import pandas as pd
pd.options.plotting.backend = "plotly"

import yfinance as yf

from cvx.simulator.builder import builder
from cvx.simulator.grid import resample_index

data = yf.download(tickers = "SPY AAPL GOOG MSFT",  # list of tickers
                   period = "10y",                   # time period
                   interval = "1d",                 # trading interval
                   prepost = False,                 # download pre/post market hours data?
                   repair = True)                   # repair obvious price errors e.g. 100x?

[                       0%%                      ]

[**********************50%%                      ]  2 of 4 completed

[**********************75%%**********            ]  3 of 4 completed

[*********************100%%**********************]  4 of 4 completed

prices = data["Adj Close"]

capital = 1e6

b = builder(prices=prices, initial_cash=capital)

for time, state in b:
    # each day we invest a quarter of the capital in the assets
    b[time[-1]] = 0.25 * state.nav / state.prices

portfolio = b.build()
portfolio.profit.cumsum().plot()

portfolio.nav.plot()

Rebalancing

Usually we would not execute on a daily basis but rather rebalance every week, month or quarter. There are two approaches to deal with this problem in cvxsimulator.

• Resample the existing daily portfolio (helpful to see effect of your hesitated trading)

• Trade only on days that are within a predefined grid (most flexible if you have a rather irregular grid)

Resample an existing portfolio

portfolio_resampled = portfolio.resample(rule="M")

frame = pd.DataFrame({"original": portfolio.nav, "monthly": portfolio_resampled.nav})
frame

	original	monthly
Date
2013-10-28	1.000000e+06	1.000000e+06
2013-10-29	9.999857e+05	9.999857e+05
2013-10-30	1.001458e+06	1.001323e+06
2013-10-31	9.988213e+05	9.987009e+05
2013-11-01	9.981312e+05	9.980087e+05
...	...	...
2023-10-23	7.064971e+06	7.047425e+06
2023-10-24	7.117703e+06	7.100342e+06
2023-10-25	6.951941e+06	6.932309e+06
2023-10-26	6.778848e+06	6.757513e+06
2023-10-27	6.794047e+06	6.773228e+06

2518 rows × 2 columns

print(portfolio_resampled.stocks)

                    AAPL          GOOG         MSFT          SPY
Date                                                            
2013-10-28  15136.661516   9889.145480  8392.967509  1702.018560
2013-10-29  15136.661516   9889.145480  8392.967509  1702.018560
2013-10-30  15136.661516   9889.145480  8392.967509  1702.018560
2013-10-31  15136.661516   9889.145480  8392.967509  1702.018560
2013-11-01  15394.545496   9754.950851  8386.712805  1699.030713
...                  ...           ...          ...          ...
2023-10-23  10106.547810  12991.142309  5456.845086  4109.458454
2023-10-24  10106.547810  12991.142309  5456.845086  4109.458454
2023-10-25  10106.547810  12991.142309  5456.845086  4109.458454
2023-10-26  10106.547810  12991.142309  5456.845086  4109.458454
2023-10-27  10106.547810  12991.142309  5456.845086  4109.458454

[2518 rows x 4 columns]

# almost hard to see that difference between the original and resampled portfolio
frame.plot()

# number of shares traded
portfolio_resampled.trades_stocks.iloc[1:].plot()

Trade only days in predefined grid

b = builder(prices=prices, initial_cash=capital)

# define a grid
grid = resample_index(prices.index, rule="M")

for time, state in b:
    # each day we invest a quarter of the capital in the assets
    if time[-1] in grid:
        b[time[-1]] = 0.25 * state.nav / state.prices
    else:
        # forward fill an existing position
        b[time[-1]] = b[time[-2]]
        
portfolio = b.build()

portfolio.nav.plot()

# Trading only once a month can lead to days where 150k had to be reallocated
portfolio.turnover.iloc[1:].plot()

Why not resampling the prices?

I don’t believe in bringing the prices to a monthly grid. This would render it hard to construct signals given the sparse grid. We stay on a daily grid and trade once a month.